1. Field of the Invention
The present invention relates to a piezoelectric resonator, particularly to a tuning fork quartz crystal resonator.
2. Related Art
A quartz crystal resonator uses its piezoelectric characteristics to generate a periodic constant frequency. It retains a relative high Quality Factor (Q value) to maintain a stable frequency. It has been provided to frequency and timing control for various portable devices such as watches, cell phones, global position system, wireless communications, and medical devices, etc.
FIG. 15 depicts the electric equivalent circuit of the quartz crystal resonator. In FIG. 15, a motional resistance (R1), a motional inductance (L1), and a motional capacitance (C1) form a series arm. This series arm is then connected to a static capacitance (C0) in parallel.
Based on the electric equivalent circuit shown in FIG. 15, the series resonate frequency (Fs) is defined as follows:
  Fs  =      1          2      ⁢      π      ⁢                                    L            1                    ⁢                      C            1                              
A tuning fork quartz crystal resonator has the same electric equivalent circuit. A tuning fork quartz crystal resonator is manufactured from a quartz wafer that was cut from a single crystal alpha quartz bar with a designate cutting angle θ. After the resonator was processed and shaped into a tuning fork structure of the desired dimension, two electrodes of opposite polarities are formed on the resonating arms with proper electrical connection paths. By inserting a tuning fork quartz crystal resonator into an oscillation circuit, it induces the resonator to vibrate in flexure mode at constant oscillating frequency.
FIG. 14 illustrates the X, Y, and Z coordinate for a single crystal alpha quartz bar, and the X, Y′, and Z′ coordinate for a quartz wafer with a designate cutting angle θ. The tuning fork crystal resonator and the quartz wafer have the same X, Y′, and Z′ coordinates. The cutting angle θ is an angle rotating around the +X axis in a range of −6° to +6°. The X axis is interpreted as an electrical axis, the Y axis is a mechanical axis, and the Z axis is an optical axis.
The resonating frequency (Fs) of the tuning fork quartz crystal resonator is proportional to the width (W) of the resonating arm, and inversely proportional to the square of the length (L) of the resonating arm. The relation of the resonating frequency, resonating arm length, and width is as follow:
  Fs  =      k    ×          W              L        2            where k is a constant.
An oscillator consists of a tuning fork quartz crystal resonator and an oscillation circuit. In general, an oscillator has a better performance when the resonator has a lower R1 value.
The electronic industry has been growing for last thirty years. On demand, most electronic devices and components have been miniaturized. A tuning fork quartz crystal resonator can be miniaturized by reducing the length and width of the resonating arms. In general, reducing the length and width of the resonating arms results in a lower C1 value and higher R1 value.